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This book investigates compressive sensing techniques to provide a robust and general framework for network data analytics. The goal is to introduce a compressive sensing framework for missing data interpolation, anomaly detection, data segmentation and activity recognition, and to demonstrate its benefits.
Chapter 1 introduces compressive sensing, including its definition, limitation, and how it supports different network analysis applications.
Chapter 2 demonstrates the feasibility of compressive sensing in network analytics, the authors we apply it to detect anomalies in the customer care call dataset from a Tier 1 ISP in the United States. A regression-based model is applied to find the relationship between calls and events. The authors illustrate that compressive sensing is effective in identifying important factors and can leverage the low-rank structure and temporal stability to improve the detection accuracy.
Chapter 3 discusses that there are several challenges in applying compressive sensing to real-world data. Understanding the reasons behind the challenges is important for designing methods and mitigating their impact. The authors analyze a wide range of real-world traces. The analysis demonstrates that there are different factors that contribute to the violation of the low-rank property in real data. In particular, the authors find that (1) noise, errors, and anomalies, and (2) asynchrony in the time and frequency domains lead to network-induced ambiguity and can easily cause low-rank matrices to become higher-ranked. To address the problem of noise, errors and anomalies in Chap. 4, the authors propose a robust compressive sensing technique. It explicitly accounts for anomalies by decomposing real-world data represented in matrix form into a low-rank matrix, a sparse anomaly matrix, an error term and a small noise matrix.
Chapter 5 addresses the problem of lack of synchronization, and the authors propose a data-driven synchronization algorithm. It can eliminate misalignment while taking into account the heterogeneity of real-world data in both time and frequency domains. The data-driven synchronization can be applied to any compressive sensing technique and is general to any real-world data. The authors illustrates that the combination of the two techniques can reduce the ranks of real-world data, improve the effectiveness of compressive sensing and have a wide range of applications